Application of elastic fluids in hydraulic fracturing implementing a physics-based analytical tool

1. A method implemented with a fracturing system to hydraulically fracture a completion interval in a formation, the method comprising:

obtaining completion parameters characterizing the completion interval;

obtaining formation parameters characterizing the formation;

obtaining fluid parameters characterizing an elastic fluid for the hydraulic fracturing by:

(i) defining regions of behavior for the elastic fluid relating shear rate relative to viscosity of the elastic fluid, the regions of behavior including (a) a viscous region defined by a threshold of the shear rate at which the Power Law applies to the elastic fluid and including (b) an elastic region defined by storage modulus (G′) relative to loss modulus (G″), by calculating the threshold of the shear rate at which the Power Law applies to the elastic fluid based on: a first differential equation of the viscosity with respect to shear rate:

δμ

δγ

,

 a second differential equation of a flow index (n′) of the Power Law with respect to shear rate:

δ

⁢

n

⁢

′

δγ

,

 and a third differential equation of the storage modulus (G′) of the elastic fluid with respect to shear rate

δ

⁢

G

⁢

′

δγ

,

 and

(ii) defining, according to the regions of behavior, friction performance of the elastic fluid relating fiction gradient relative to flow rate of the elastic fluid;

determining fracturing parameters for the hydraulic fracturing by modeling the hydraulic fracturing with the elastic fluid in the completion interval in the formation based on the formation parameters, the completion parameters, and the fluid parameters; and

performing an operation of the hydraulic fracturing with the elastic fluid in the completion interval using the determined fracturing parameters.

2. The method of claim 1 , wherein defining the regions of behavior comprises performing an oscillation test on the elastic fluid to define elastic modules.

3. The method of claim 1 , wherein defining, according to the regions of behavior, the friction performance of the elastic fluid relating the fiction gradient relative to the flow rate of the elastic fluid comprises determining the friction performance in two different friction segments, a first of the friction segments for the viscous region defined by the Power Law, and a second of the friction segment for the elastic region defined by the storage modulus (G′) relative to the loss modulus (G″).

4. The method of claim 1 , wherein defining, according to the regions of behavior, the friction performance of the elastic fluid relating the fiction gradient relative to the flow rate of the elastic fluid comprises performing friction loop testing of the elastic fluid in a plurality of pipe sizes at a plurality of different ones of the flow rates; and estimating a plurality of the friction gradient of the elastic fluid at the different flow rates for the plurality of pipe sizes.

5. The method recited in claim 1 , wherein defining, according to the regions of behavior, the friction performance of the elastic fluid relating the fiction gradient relative to the flow rate of the elastic fluid comprises:

obtaining experimental data points in terms of Reynolds number at different shear rate stations in friction flow loop testing, wherein Reynolds number is measured at each stabilized step; and

computing pressure losses with the experimental data at the different shear rate stations to produce a pressure mathematical model that correlates with pressure drop hydraulics.

6. The method recited in claim 5 , wherein computing the pressure losses comprises processing the experimental data in a hydraulics model to find a best curve fit combining the Reynolds number and the shear rate for each of the stations in the elastic region of the behavior of the elastic fluid defined by the storage modulus (G′) being greater than the loss modulus (G″).

7. The method of claim 6 , wherein modeling the hydraulic fracturing with the elastic fluid in the completion interval based on the formation parameters, the completion parameters, and the fluid parameters comprises modeling flow restrictions in the completion interval and calculating the pressure losses of the elastic fluid pumped at a pump rate through the modeled flow restrictions.

8. The method of claim 1 , wherein obtaining the fluid parameters of the elastic fluid further comprises:

obtaining experimental data of a suspension capacity of the elastic fluid;

using the experimental data in a 3D Model suspension test run up to a maximum concentration by combining the experimental data with elasticity and viscosity parameters of the elastic fluid, and calibrating a proppant transport model for the elastic fluid with numerical simulations for particle settling based on coupled Computational Fluid Dynamics (CFD) and Discrete Element Methods (DEMs); and

quantifying a proppant-carrying capacity of the elastic fluid based on the proppant transport model for the elastic fluid.

9. The method of claim 8 , further comprising quantifying the proppant-carrying capacity of the elastic fluid with respect to density by performing numeric analysis.

10. The method of claim 8 , further comprising quantify the proppant-carrying capacity of the elastic fluid with respect to various proppant types and concentrations by performing numeric analysis.

11. The method of claim 1 , wherein modeling the hydraulic fracturing with the elastic fluid in the completion interval in the formation based on the formation parameters, the completion parameters, and the fluid parameters comprises optimizing the fracturing parameters based on a selection of the elastic fluid, a proppant type, a proppant concentration, and a pumping rate according to a stimulation objective.

12. The method of claim 1 , wherein modeling the hydraulic fracturing with the elastic fluid in the completion interval based on the formation parameters, the completion parameters, and the fluid parameters comprises modelling based on one or more of: reservoir depth, pore pressure gradient, porosity, permeability, total organic carbon (TOC), water saturation, Young's modulus, Poisson's ratio, rock strength, cohesion, and sh-min gradient.

13. The method of claim 1 , wherein modeling the hydraulic fracturing comprises one or more of:

performing a simulation to predict hydraulic fracture propagation, fracture height growth, and natural fracture reactivation;

performing a simulation to model proppant transport within both main hydraulic fractures and a reactivated natural fracture network;

performing a simulation to assess proppant embedment and crush-fracture surface closure behavior during production; and

performing a simulation to forecast production efficiency.

14. The method recited in claim 1 , wherein determining the fracturing parameters comprises determining a modified pumping schedule.

15. The method of claim 14 , wherein determining the modified pumping schedule comprises changing an injection time, a rate, a proppant type, a viscosity of the elastic fluid at different shear rates, and a density of the elastic fluid.

16. The method of claim 1 , wherein performing the operation of the hydraulic fracturing with the elastic fluid in the completion interval using the determined fracturing parameters comprises pumping the elastic fluid at least in the completion interval according one or more of a pressure, stimulation time, a fluid density, a fluid viscosity, a proppant density, and a proppant diameter from the determined fracturing parameters.

17. The method of claim 1 , further comprising:

obtaining field data of the elastic fluid by assessing the performance of the hydraulic fracturing; and

updating the fluid parameters of the elastic fluid based on the obtained field data.

18. The method of claim 17 , wherein obtaining the field data comprises collecting friction data at different rates and flow path restrictions; and wherein updating the fluid parameters comprises improving the determination of the friction performance of the elastic fluid with the collected friction data at the different flow rates and the flow path restrictions.

19. A programmable storage device having program instructions stored thereon for causing a programmable control device to perform a method to hydraulically fracture a completion interval in a formation according to claim 1 .

20. A method implemented with a fracturing system to hydraulically fracture a completion interval in a formation, the method comprising:

obtaining completion parameters characterizing the completion interval;

obtaining formation parameters characterizing the formation;

obtaining fluid parameters characterizing an elastic fluid for the hydraulic fracturing by:

(i) defining regions of behavior for the elastic fluid relating shear rate relative to viscosity of the elastic fluid, the regions of behavior including a viscous region defined by the Power Law and including an elastic region defined by storage modulus (G′) relative to loss modulus (G″), and

(ii) defining, according to the regions of behavior, friction performance of the elastic fluid relating fiction gradient relative to flow rate of the elastic fluid by:

(a) obtaining experimental data points in terms of Reynolds number at different shear rates in friction flow loop testing, wherein Reynolds number is measured at each stabilized step; and

(b) computing pressure losses with the experimental data at the different shear rates to produce a pressure mathematical model that correlates with pressure drop hydraulics;

determining fracturing parameters for the hydraulic fracturing by modeling the hydraulic fracturing with the elastic fluid in the completion interval in the formation based on the formation parameters, the completion parameters, and the fluid parameters; and

performing an operation of the hydraulic fracturing with the elastic fluid in the completion interval using the determined fracturing parameters.

21. The method of claim 20 , wherein computing the pressure losses comprises processing the experimental data in a hydraulics model to find a best curve fit combining the Reynolds number and the shear rates in the elastic region of the behavior of the elastic fluid defined by the storage modulus (G′) being greater than the loss modulus (G″).

22. The method of claim 20 , wherein modeling the hydraulic fracturing with the elastic fluid in the completion interval based on the formation parameters, the completion parameters, and the fluid parameters comprises modeling flow restrictions in the completion interval and calculating the pressure losses of the elastic fluid pumped at a pump rate through the modeled flow restrictions.

23. A method implemented with a fracturing system to hydraulically fracture a completion interval in a formation, the method comprising:

obtaining completion parameters characterizing the completion interval;

obtaining formation parameters characterizing the formation;

obtaining fluid parameters characterizing an elastic fluid for the hydraulic fracturing by:

(i) defining regions of behavior for the elastic fluid relating shear rate relative to viscosity of the elastic fluid, the regions of behavior including a viscous region defined by the Power Law and including an elastic region defined by storage modulus (G′) relative to loss modulus (G″),

(ii) defining, according to the regions of behavior, friction performance of the elastic fluid relating fiction gradient relative to flow rate of the elastic fluid;

(iii) obtaining experimental data of a suspension capacity of the elastic fluid;

(iv) calibrating a proppant transport model for the elastic fluid using the experimental data combined with elasticity and viscosity parameters of the elastic fluid; and

(v) quantifying a proppant-carrying capacity of the elastic fluid based on the proppant transport model for the elastic fluid;

determining fracturing parameters for the hydraulic fracturing by modeling the hydraulic fracturing with the elastic fluid in the completion interval in the formation based on the formation parameters, the completion parameters, and the fluid parameters; and

performing an operation of the hydraulic fracturing with the elastic fluid in the completion interval using the determined fracturing parameters.

24. The method of claim 23 , wherein calibrating the proppant transport model for the elastic fluid using the experimental data combined with the elasticity and viscosity parameters of the elastic fluid comprises using the experimental data in a 3D Model suspension test run up to a maximum concentration by combining the experimental data with elasticity and viscosity parameters of the elastic fluid, and calibrating the proppant transport model for the elastic fluid with numerical simulations for particle settling based on coupled Computational Fluid Dynamics (CFD) and Discrete Element Methods (DEMs).

25. The method of claim 23 , further comprising quantifying the proppant-carrying capacity of the elastic fluid with respect to density by performing numeric analysis.

26. The method of claim 23 , further comprising quantify the proppant-carrying capacity of the elastic fluid with respect to various proppant types and concentrations by performing numeric analysis.

27. A method implemented with a fracturing system to hydraulically fracture a completion interval in a formation, the method comprising:

obtaining completion parameters characterizing the completion interval;

obtaining formation parameters characterizing the formation;

obtaining fluid parameters characterizing an elastic fluid for the hydraulic fracturing by:

(i) defining regions of behavior for the elastic fluid relating shear rate relative to viscosity of the elastic fluid, the regions of behavior including a viscous region defined by the Power Law and including an elastic region defined by storage modulus (G′) relative to loss modulus (G″), and

(ii) defining, according to the regions of behavior, friction performance of the elastic fluid relating fiction gradient relative to flow rate of the elastic fluid by:

(a) obtaining experimental data points in terms of Reynolds number at different shear rates; and

(b) computing pressure losses with the experimental data at the different shear rates by processing the experimental data in a hydraulics model to find a best curve fit combining the Reynolds number and the shear rates in the elastic region of the behavior of the elastic fluid defined by the storage modulus (G′) being greater than the loss modulus (G″);

determining fracturing parameters for the hydraulic fracturing by modeling the hydraulic fracturing with the elastic fluid in the completion interval in the formation based on the formation parameters, the completion parameters, and the fluid parameters; and

performing an operation of the hydraulic fracturing with the elastic fluid in the completion interval using the determined fracturing parameters.

28. The method of claim 27 , wherein modeling the hydraulic fracturing with the elastic fluid in the completion interval based on the formation parameters, the completion parameters, and the fluid parameters comprises modeling flow restrictions in the completion interval and calculating the pressure losses of the elastic fluid pumped at a pump rate through the modeled flow restrictions.